Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Nonlinear Differential Equations and Inequalities for Ph.D. Students I - NMMO621

Title:	Nelineární diferenciální rovnice a nerovnice pro doktorandy I
Guaranteed by:	Mathematical Institute of Charles University (32-MUUK)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Miroslav Bulíček, Ph.D.
Class:	DS, matematické a počítačové modelování DS, matematická analýza
Classification:	Mathematics > Mathematical Modeling in Physics
Incompatibility :	NDIR142
Interchangeability :	NDIR142
Is interchangeable with:	NDIR142

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: G_M (07.05.2014)

Pseudomonotone and monotone operators, set-valued mappings and applications to nonlinear elliptic partial differential equations and inequalities.

Aim of the course -

Last update: G_M (07.05.2014)

To present at least a bit of Nonlinear Differential Equations and Inequalities.

Course completion requirements -

Last update: doc. RNDr. Miroslav Bulíček, Ph.D. (04.10.2018)

The exam has the oral form and is based on the lectures.

Literature - Czech

Last update: G_M (07.05.2014)

T.Roubícek: Nonlinear Partial Differential Equations with Applications. Birkhauser, Basel, 2005.

Teaching methods -

Last update: G_M (07.05.2014)

Lecture

Requirements to the exam -

Last update: doc. RNDr. Miroslav Bulíček, Ph.D. (04.10.2018)

There will be an oral exam. The exam is based on the lectures.

Syllabus -

Last update: G_M (07.05.2014)

The goal is a presentation of fundamental techniques used for nonlinear differential equations and inequalities both on the level of abstract mappings in Banach spaces and on the typical cases derived as weak formulations of steady-state boundary-value or unilateral problems or free-boundary problems for quasi- or semi-linear elliptic partial differential equations. In particular, methods of monotonicity and compactness, variational methods for problem with (possibly nonsmooth) potentials, Galerkin's method, and the penalty method will be addressed, as well as systems of nonlinear differential equations with definite applications in (thermo)mechanics of continua or other areas of physics.

Exercises will involve modifications of problems presented in the main course.

Entry requirements -

Last update: doc. RNDr. Miroslav Bulíček, Ph.D. (04.10.2018)

Basic knowledge of theory of weak solutions to linear elliptic equations.